One line passes through the points $(-8,1)$ and $(4,4)$. Another line passes through points $(-9,-7)$ and $(9,-3)$.

Are the lines parallel, perpendicular, or neither?
Choose 1 answer:
(A) Parallel
B) Perpendicular
(C) Neither

Question

One line passes through the points $(-8,1)$ and $(4,4)$. Another line passes through points $(-9,-7)$ and $(9,-3)$.

Are the lines parallel, perpendicular, or neither?
Choose 1 answer:
(A) Parallel
B) Perpendicular
(C) Neither

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine if the lines are parallel, perpendicular, or neither, we need to compare their slopes. ‖ ‖ step 2 ⋮ The slope of the line through points $(-8,1)$ and $(4,4)$ is calculated as $\frac{4 - 1}{4 - (-8)} = \frac{3}{12} = \frac{1}{4}$. ‖ ‖ step 3 ⋮ The slope of the line through points $(-9,-7)$ and $(9,-3)$ is calculated as $\frac{-3 - (-7)}{9 - (-9)} = \frac{4}{18} = \frac{2}{9}$. ‖ ‖ step 4 ⋮ Since the slopes $\frac{1}{4}$ and $\frac{2}{9}$ are not equal, the lines are not parallel. ‖ ‖ step 5 ⋮ To check for perpendicularity, we see if the slopes are negative reciprocals of each other. The negative reciprocal of $\frac{1}{4}$ is $-4$, which is not equal to $\frac{2}{9}$. ‖ ‖ step 6 ⋮ Since the slopes are neither equal nor negative reciprocals of each other, the lines are neither parallel nor perpendicular. ‖ ∻[1] Answer∻ ⚹ (C) Neither ⚹ ∻Key Concept∻ ⚹Slope comparison for parallelism and perpendicularity⚹ ∻Explanation∻ ⚹Two lines are parallel if they have the same slope and perpendicular if the product of their slopes is -1. In this case, the slopes are neither equal nor negative reciprocals, so the lines are neither parallel nor perpendicular.◊What is the slope of the line passing through the points $(-8, 1)$ and $(4, 4)$?⍭ Generate me a similar question◊⚹

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